An airplane is heading due south at a speed of 640 km/h. If a wind begins blowin
ID: 2025494 • Letter: A
Question
An airplane is heading due south at a speed of 640 km/h. If a wind begins blowing from the southwest at a speed of 100 km/h (average), calculate the following.(a) the velocity (magnitude and direction) of the plane relative to the ground
_________km/h _________° (east of south)
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action. [Hint: First draw a diagram.]
__________ km
Explanation / Answer
a) we model the problem as a right triangle with sides adjacent to the 90 degree angle as 640 and 100. using the pythagorean theorem, we find the magnitude of the rusulting vector v^2 = 640^2 + 100^2 -----> v = 647.765 km/h using properties of right triangles, tan(a) = 100/640 where a is the angle east of south a = 8.88 degrees east of south b) to calculate how far the pilot will be off course after 10 minutes: there are 60 min/h so, 10 min = 0.166667h the wind is blowing the plane off course at a rate of 100km/h so, after 10min, the plane is 100(km/h)*0.166667h = 16.667km to the east of its intended position